Strong decays of ${\mathrm{\ensuremath{\Xi}}}_{c}$ baryons with radial or orbital $\ensuremath{\lambda}$- and $\ensuremath{\rho}$-mode excitations with positive parity have been studied in a $^{3}{P}_{0}$ model. As candidates of these kinds of excited charmed strange baryons, possible configurations and ${J}^{P}$ quantum numbers of ${\mathrm{\ensuremath{\Xi}}}_{c}(2930)$, ${\mathrm{\ensuremath{\Xi}}}_{c}(2980)$, ${\mathrm{\ensuremath{\Xi}}}_{c}(3055)$, ${\mathrm{\ensuremath{\Xi}}}_{c}(3080)$, and ${\mathrm{\ensuremath{\Xi}}}_{c}(3123)$ have been assigned based on experimental data. There are 40 kinds of configurations to describe the first radial or orbital excited ${\mathrm{\ensuremath{\Xi}}}_{c}$ in $\ensuremath{\lambda}$- and $\ensuremath{\rho}$-mode excitations with positive parity. In these assignments, ${\mathrm{\ensuremath{\Xi}}}_{c}(2930)$ may be a $2S$-wave excited ${\stackrel{\texttildelow{}}{\mathrm{\ensuremath{\Xi}}}}_{c1}({\frac{1}{2}}^{+})$ or ${\stackrel{\texttildelow{}}{\mathrm{\ensuremath{\Xi}}}}_{c1}({\frac{3}{2}}^{+})$, or a $D$-wave excited ${\stackrel{^}{\mathrm{\ensuremath{\Xi}}}}_{c1}^{\ensuremath{'}}({\frac{1}{2}}^{+})$, ${\stackrel{\textasciicaron{}}{\mathrm{\ensuremath{\Xi}}}}_{c1}^{0}({\frac{1}{2}}^{+})$, ${\stackrel{\textasciicaron{}}{\mathrm{\ensuremath{\Xi}}}}_{c1}^{2}({\frac{1}{2}}^{+})$, ${\stackrel{^}{\mathrm{\ensuremath{\Xi}}}}_{c1}^{\ensuremath{'}}({\frac{3}{2}}^{+})$, ${\stackrel{\textasciicaron{}}{\mathrm{\ensuremath{\Xi}}}}_{c1}^{0}({\frac{3}{2}}^{+})$, or ${\stackrel{\textasciicaron{}}{\mathrm{\ensuremath{\Xi}}}}_{c1}^{2}({\frac{3}{2}}^{+})$. ${\mathrm{\ensuremath{\Xi}}}_{c}(2980{)}^{+}$ may be a $2S$-wave excited ${\stackrel{\texttildelow{}}{\mathrm{\ensuremath{\Xi}}}}_{c1}({\frac{1}{2}}^{+})$ or ${\stackrel{\texttildelow{}}{\mathrm{\ensuremath{\Xi}}}}_{c0}^{\ensuremath{'}}({\frac{1}{2}}^{+})$ with ${J}^{P}={\frac{1}{2}}^{+}$, or a $D$-wave excited ${\stackrel{\textasciicaron{}}{\mathrm{\ensuremath{\Xi}}}}_{c0}^{\ensuremath{'}0}({\frac{1}{2}}^{+})$ or ${\stackrel{\textasciicaron{}}{\mathrm{\ensuremath{\Xi}}}}_{c1}^{0}({\frac{1}{2}}^{+})$ with ${J}^{P}={\frac{1}{2}}^{+}$. ${\mathrm{\ensuremath{\Xi}}}_{c}(3055{)}^{+}$ may be a $2S$-wave excited ${\stackrel{\ifmmode\acute\else\textasciiacute\fi{}}{\mathrm{\ensuremath{\Xi}}}}_{c1}^{\ensuremath{'}}({\frac{3}{2}}^{+})$ or ${\stackrel{\ifmmode\acute\else\textasciiacute\fi{}}{\mathrm{\ensuremath{\Xi}}}}_{c0}({\frac{1}{2}}^{+})$. It may be a $D$-wave excited ${\mathrm{\ensuremath{\Xi}}}_{c1}^{\ensuremath{'}}({\frac{3}{2}}^{+})$, ${\mathrm{\ensuremath{\Xi}}}_{c2}^{\ensuremath{'}}({\frac{5}{2}}^{+})$, ${\mathrm{\ensuremath{\Xi}}}_{c2}({\frac{3}{2}}^{+})$, or ${\mathrm{\ensuremath{\Xi}}}_{c2}({\frac{5}{2}}^{+})$. ${\mathrm{\ensuremath{\Xi}}}_{c}(3080{)}^{+}$ is very possibly a $2S$-wave excited ${\stackrel{\ifmmode\acute\else\textasciiacute\fi{}}{\mathrm{\ensuremath{\Xi}}}}_{c0}({\frac{1}{2}}^{+})$ and seems not to be a $D$-wave excitation of ${\mathrm{\ensuremath{\Xi}}}_{c}$. Because of the poor experimental information for ${\mathrm{\ensuremath{\Xi}}}_{c}(3123)$, it is impossible to identify this state at present. It is found that the channel $\mathrm{\ensuremath{\Lambda}}D$ vanishes in the strong decay of $P$-wave, $D$-wave, and $2S$-wave excited ${\mathrm{\ensuremath{\Xi}}}_{c}$ without $\ensuremath{\rho}$-mode excitation between the two light quarks (${n}_{\ensuremath{\rho}}={L}_{\ensuremath{\rho}}=0$). In different configurations, some branching fraction ratios related to the internal structure of the $2S$-wave and $D$-wave of ${\mathrm{\ensuremath{\Xi}}}_{c}$ are different. These ratios have been computed and can be employed to distinguish different configurations in forthcoming experiments.
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Aug 1, 2019
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